Computer Program Detail Page

Gyroscope Model

written by
Wolfgang Christian

The Gyroscope example computes and displays the dynamics of gyroscope under the influence of a gravitational torque acting on the center of mass. The gyroscope is supported at one end and given an initial angular velocity component about its axis of symmetry and a component perpendicular to its axis of symmetry. The numerical solution shows the motion for all initial conditions including zero initial angular momentum. The model is designed to show the cycloidal motion (precession and nutation) of the gyroscope axle when the initial angular velocity is large. Users can very the position and radius of the spinning mass as well as the initial angle and can display the angular momentum, angular velocity, and torque vectors. A second window shows the elevation angle of the axle and the angular momentum vector.

Units are chosen such that the total mass M and the acceleration of gravity g are one. The rotor is an ellipsoid with a uniform mass distribution and with major axes 2*R and minor axis R/5. The ellipsoid's moment of inertia through the center of mass is 4MR2/5 about the major axes and 26MR2/125 about the minor axis.

The Gyroscope model is a supplemental simulation for the article "It Has to Go Down a Little, in Order to Go Around" by Svilen Kostov and Daniel Hammer in The Physics Teacher 49(4), 216-219 (2011) and has been approved by the authors and The Physics Teacher editor. The model was developed using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_csm_ch17_Gyroscope.jar file will run the program if Java is installed.

Gyroscope Source Code
The source code zip archive contains an XML representation of the Gyroscope model. Unzip this archive in your EJS workspace to compile and run this model… more...download 260kb .zip
Last Modified: February 10, 2011

Standards (2)

AAAS Benchmark Alignments (2008 Version)

4. The Physical Setting

4E. Energy Transformations

6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.

AAAS Benchmark Alignments (1993 Version)

4. THE PHYSICAL SETTING

E. Energy Transformations

4E (9-12) #2. Heat energy in a material consists of the disordered motions of its atoms or molecules. In any interactions of atoms or molecules, the statistical odds are that they will end up with less order than they began?that is, with the heat energy spread out more evenly. With huge numbers of atoms and molecules, the greater disorder is almost certain.

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